Multi-port Stowage Optimization With Consideration Of Deck Constraint And Ship Balance

The stowage quality of container ships at each port has a significant impact on the cost and efficiency of the ship transportation.How to decrease the re-shift number of containers and how to reduce the imbalance of the ship are the two key factors impacting the loading efficiency and the transportation cost.Multiple ports to visit,a great number of containers to move,the large scale of ships,and the consideration of deck blockage are among the main factors that make this problem quite complex.Containers are discharged in a downward sequence from the upper tier to the lower one.When a container arrives at its destination port,all the containers located above need to be unloaded no matter whether or not they arrive at the destination.Those unloaded containers whose destination is not the current port need to be reloaded onto the vessel.This operation is called re-shift movement,and should be avoided as far as possible.In the presence of decks,all the containers above the deck need to be unloaded when a container under the deck is unloaded.Therefore,the deck blockage has a significant impact on the re-shifting of containers.This practical feature will be considered in this paper.On the other hand,a containership has to maintain its balance both in the horizontal and in the vertical direction to prevent it from capsizing.Improper stowage planning may cause the imbalance of the containership severely towards one side.To ensure safety,water is usually injected to the opposite side of the ship to reduce the imbalance.The injected water not only wastes partial space but also increases energy consumption.As a result,reducing the imbalance of the ship when making the stowage plan is necessary for the economic benefit.In this paper,we will take into consideration the vertical and horizontal imbalance calculated by the torque when loading the containers.We take into consideration the reduction both in the re-shifting movements and the imbalance of ship hull.An integer programming model is built with the objective of minimizing the number of re-shifting movements,subject to the imbalance threshold imposed on containerships.A heuristic algorithm is proposed to calculate the re-shift movements besides the CPLEX which directly runs on the built integer program.In the heuristic,the imbalance of the ship is checked after loading a certain number of containers,and the subsequent loading strategy will be adjusted according to the newly calculated imbalance of the ship.The numerical results show that our algorithm is effective and viable to the problem.